Temperature regulation of marine mammals

A mathematical model of heat loss from an aquatic animal to the surrounding water is presented. Heat is generated in metabolically active tissues and distributed by circulating blood and by conduction. The time dependent radial temperature profile of the animal is numerically solved from heat transfer equations by a computer. The model is applied to large whales, porpoises, and seals. For the whales, blood circulation to the dermal layer below appendage and body skin surfaces proved to be essential for sufficient heat dissipation. When decreasing the blood flow below a certain value (dependent on sea temperature and whale activity) the large whales would overheat. Blubber thickness was found to be of minor importance in whale thermoregulation, because the blubber coat can be bypassed by blood circulation. On the other hand, it is in general not possible for small porpoises and seals to stay warm in the coldest waters using normal mammalian resting metabolic rates, even if the peripheral circulation is shut off (or artery-vein heat exchangers used). Heat loss can be reduced if the outermost tissue layers are allowed to cool. This is achieved by minimizing convective radial heat flow via the circulation. (For large whales even minute radial blood flow raises the muscle temperatures to the core temperature level.) Seasonal acclimatization of harbour seals is explained by changes in their effective insulation thickness. Differences in whale activity induce changes in the temperature profile mainly within the first few centimeters from the skin surface. These superficial temperatures, if known, could be used to estimate whale metabolic rates. Since they drop close to the sea water temperature within minutes after whale death, the measurements should be done of live whales.     

Heat transfer in a microvascular network: the effect of heart rate on heating and cooling in reptiles (Pogona barbata and Varanus varius)

Thermally-induced changes in heart rate and blood flow in reptiles are believed to be of selective advantage by allowing animal to exert some control over rates of heating and cooling. This notion has become one of the principal paradigms in reptilian thermal physiology. However, the functional significance of changes in heart rate is unclear, because the effect of heart rate and blood flow on total animal heat transfer is not known. I used heat transfer theory to determine the importance of heat transfer by blood flow relative to conduction. I validated theoretical predictions by comparing them with field data from two species of lizard, bearded dragons (Pogona barbata) and lace monitors (Varanus varius). Heart rates measured in free-ranging lizards in the field were significantly higher during heating than during cooling, and heart rates decreased with body mass. Convective heat transfer by blood flow increased with heart rate. Rates of heat transfer by both blood flow and conduction decreased with mass, but the mass scaling exponents were different. Hence, rate of conductive heat transfer decreased more rapidly with increasing mass than did heat transfer by blood flow, so that the relative importance of blood flow in total animal heat transfer increased with mass. The functional significance of changes in heart rate and, hence, rates of heat transfer, in response to heating and cooling in lizards was quantified. For example, by increasing heart rate when entering a heating environment in the morning, and decreasing heart rate when the environment cools in the evening a Pogona can spend up to 44 min longer per day with body temperature within its preferred range. It was concluded that changes in heart rate in response to heating and cooling confer a selective advantage at least on reptiles of mass similar to that of the study animals (0. 21-5.6 kg).     

A canine thermal model for simulating temperature responses of military working dogs

Military working dogs (MWDs) are often required to operate in dangerous or extreme environments, to include hot and humid climate conditions. These scenarios can put MWD at significant risk of heat injury. To address this concern, a two-compartment (core, skin) rational thermophysiological model was developed to predict the temperature of a MWD during rest, exercise, and recovery. The Canine Thermal Model (CTM) uses inputs of MWD mass and length to determine a basal metabolic rate and body surface area. These calculations are used along with time series inputs of environmental conditions (air temperature, relative humidity, solar radiation and wind velocity) and level of metabolic intensity (MET) to predict MWD thermoregulatory responses. Default initial values of core and skin temperatures are set at neutral values representative of an average MWD; however, these can be adjusted to match known or expected individual temperatures. The rational principles of the CTM describe the heat exchange from the metabolic energy of the core compartment to the skin compartment by passive conduction as well as the application of an active control for skin blood flow and to tongue and lingual tissues. The CTM also mathematically describes heat loss directly to the environment via respiration, including panting. Thermal insulation properties of MWD fur are also used to influence heat loss from skin and gain from the environment. This paper describes the CTM in detail, outlining the equations used to calculate avenues of heat transfer (convective, conductive, radiative and evaporative), overall heat storage, and predicted responses of the MWD. Additionally, this paper outlines examples of how the CTM can be used to predict recovery from exertional heat strain, plan work/rest cycles, and estimate work duration to avoid overheating.     

Physical constraints on temperature difference in some thermogenic aroid inflorescences

* BACKGROUNDS AND AIMS: Thermogenesis in reproductive organs is known from several plant families, including the Araceae. A study was made of the relationship between temperature increase and spadix size in the subfamily Aroideae in order to determine whether the quantitative variation of heat production among species and inflorescences of different sizes follows a physical law of heat transfer. * METHODS: Spadix temperature was measured in 18 species from eight genera of tropical Araceae from the basal clade of Aroideae, both in French Guiana and in the glasshouses of the Montreal Botanical Garden. * KEY RESULTS: A significant logarithmic relationship was found between the volume of the thermogenic spadix zone and the maximum temperature difference between the spadix and ambient air. Four heat transfer models were applied to the data (conductive heat transfer alone, convective heat transfer alone, radiative heat transfer alone, and convective and radiative heat transfers) to test if physical (geometric and thermic) constraints apply. Which heat transfer model was the most probable was determined by using the criterion of a classical minimization process represented by the least-squares method. Two heat transfer models appeared to fit the data well and were equivalent: conductive heat transfer alone, and convective plus radiative heat transfers. * CONCLUSIONS: The increase in the temperature difference between the spadix and ambient air appears to be physically constrained and corresponds to the value of a thermal model of heat conduction in an insulated cylinder with an internal heat source. In the models, a heat metabolic rate of 29.5 mW g(-1) was used, which was an acceptable value for an overall metabolic heat rate in aroid inflorescences.     

Physiological thermoregulation in a crustacean? Heart rate hysteresis in the freshwater crayfish Cherax destructor

Differential heart rates during heating and cooling (heart rate hysteresis) are an important thermoregulatory mechanism in ectothermic reptiles. We speculate that heart rate hysteresis has evolved alongside vascularisation, and to determine whether this phenomenon occurs in a lineage with vascularised circulatory systems that is phylogenetically distant from reptiles, we measured the response of heart rate to convective heat transfer in the Australian freshwater crayfish, Cherax destructor. Heart rate during convective heating (from 20 to 30 degrees C) was significantly faster than during cooling for any given body temperature. Heart rate declined rapidly immediately following the removal of the heat source, despite only negligible losses in body temperature. This heart rate 'hysteresis' is similar to the pattern reported in many reptiles and, by varying peripheral blood flow, it is presumed to confer thermoregulatory benefits particularly given the thermal sensitivity of many physiological rate functions in crustaceans.     

Penetration of external thermal perturbations into homeothermic organisms, part I (author's transl)

The general importance of the mean surface curvature for heat conduction problems is explained and a special symmetry with constant mean curvature on the isothermal surfaces is defined. The applicability for the body shapes of homeothermic organisms is demonstrated and the partial differential equation of heat conduction for this case is derived. The definition: heat release = real heat production + convective pseudoproduction eliminates the term of convective heat transfer through the blood stream and allows the reduction to a mere heat conduction problem. Formulas for the heat loss to the environment and for steady state temperature profiles are given. In case of sudden change of heat loss the partial differential equation is solved and a formula is derived, using dimensionless coordinates of time and distance. The mean surface curvature has strongest influence to the interior temperature field. The solution shows clearly the importance of thermal inertia of the homeothermic organism, for the external temperature wave penetrates into the body with a long phase displacement in time.     

Deep body and surface temperature responses to hot and cold environments in the zebra finch

Global warming increasingly challenges thermoregulation in endothermic animals, particularly in hot and dry environments where low water availability and high temperature increase the risk of hyperthermia. In birds, un-feathered body parts such as the head and bill work as ‘thermal windows’, because heat flux is higher compared to more insulated body regions. We studied how such structures were used in different thermal environments, and if heat flux properties change with time in a given temperature. We acclimated zebra finches (Taeniopygia guttata) to two different ambient temperatures, ‘cold’ (5 °C) and ‘hot’ (35 °C), and measured the response in core body temperature using a thermometer, and head surface temperature using thermal imaging. Birds in the hot treatment had 10.3 °C higher head temperature than those in the cold treatment. Thermal acclimation also resulted in heat storage in the hot group: core body temperature was 1.1 °C higher in the 35 °C group compared to the 5 °C group. Hence, the thermal gradient from core to shell was 9.03 °C smaller in the hot treatment. Dry heat transfer rate from the head was significantly lower in the hot compared to the cold treatment after four weeks of thermal acclimation. This reflects constraints on changes to peripheral circulation and maximum body temperature. Heat dissipation capacity from the head region increased with acclimation time in the hot treatment, perhaps because angiogenesis was required to reach peak heat transfer rate. We have shown that zebra finches meet high environmental temperature by heat storage, which saves water and energy, and by peripheral vasodilation in the head, which facilitates dry heat loss. These responses will not exclude the need for evaporative cooling, but will lessen the amount of energy expend on body temperature reduction in hot environments.     

Endothermy in fishes: a phylogenetic analysis of constraints,predispositions, and selection pressures

Synopsis Endothermy, the ability to raise body temperature by internal heat production, is unusual in teleost fishes and has only been documented within one suborder, the Scombroidei. Two separate modes of endothermy have evolved in the scombroidei; tunas warm their muscles, brain and viscera using heat exchangers in the circulation to these metabolically active tissues while billfishes and one primitive mackerel have a thermogenic organ situated beneath the brain. Both modes of endothermy emphasize common themes. Large body size coupled with heat exchangers are necessary to reduce convective and conductive heat exchange. A tissue with a high oxidative capacity is required for heat generation. Studies based upon morphology and mitochondrial DNA analyses indicate that endothermy has evolved independently at least three times within the scombroid lineage. Mapping of-morphological and physiological traits on a molecular phylogeny for scombroids provides evidence of selective pressures favoring evolution of diverse endothermic styles. The new results suggest anatomical constraints prevent most fish from using the tuna form of endothermy and indicate a possible linkage between endothermy and locomotory style (thunniform or sub-carangiform).Paper from the International Union of Biological Societies symposium The biology of tunas and billfishes: an examination of life on the knife edge, organized by Richard W. Brill and Kim N. Holland.     

Theory on thermal probe arrays for the distinction between the convective and the perfusive modalities of heat transfer in living tissues

Recent suggestions for an improved model of heat transfer in living tissues emphasize the existence of a convective mode due to flowing blood in addition to, or even instead of, the perfusive mode, as proposed in Pennes' "classic" bioheat equation. In view of these suggestions, it might be beneficial to develop a technique that will enable one to distinguish between these two modes of bioheat transfer. To this end, a concept that utilizes a multiprobe array of thermistors in conjunction with a revised bioheat transfer equation has been derived to distinguish between, and to quantify the perfusive and convective contribution of blood to heat transfer in living tissues. The array consists of two or more temperature sensors one of which also serves to locally insert a short pulse of heat into the tissue prior to the temperature measurements. A theoretical analysis shows that such a concept is feasible. The construction of the system involves the selection of several important design parameters, i.e., the distance between the probes, the heating power, and the pulse duration. The choice of these parameters is based on computer simulations of the actual experiment.     

Conditions for equivalency of countercurrent vessel heat transfer formulations.

Previous models of countercurrent blood vessel heat transfer have used one of two, different, equally valid but previously unreconciled formulations, based either on: (1) the difference between the arterial and venous vessels' average wall temperatures, or (2) the difference between those vessels' blood bulk fluid temperatures. This paper shows that these two formulations are only equivalent when the four, previously undefined, "convective heat transfer coefficients" that are used in the bulk temperature difference formulation (two coefficients each for the artery and vein) have very specific, problem-dependent relationships to the standard convective heat transfer coefficients. (The average wall temperature formulation uses those standard coefficients correctly.) The correct values of these bulk temperature difference formulation "convective heat transfer coefficients" are shown to be either: (1) specific functions of (a) the tissue conduction resistances, (b) the standard convective heat transfer coefficients, and (c) the independently specified bulk arterial, bulk venous and tissue temperatures, or (2) arbitrary, user defined values. Thus, they are generally not equivalent to the standard convective heat transfer coefficients that are regularly used, and must change values depending on the blood and tissue temperatures. This dependence can significantly limit the convenience and usefulness of the bulk temperature difference formulations.     

Numerical simulation for heat transfer in tissues during thermal therapy

In this paper, a mathematical model describing the process of heat transfer in biological tissues for different coordinate system during thermal therapy by electromagnetic radiation is studied. The boundary value problem governing this process has been solved using Galerkin’s method taking B-polynomial as basis function. The system of ordinary differential equation in unknown time variable, thus obtained, is solved by homotopy perturbation method. The effect of thermal conductivity, antenna power constant, surface temperature, and blood perfusion rate on temperature for different coordinates are discussed. It has been observed that the process is faster in spherical symmetric coordinates in comparison to axisymmetric coordinate and faster in axisymmetric in comparison to Cartesian coordinate.     

Computational fluid dynamics analysis of drag and convective heat transfer of individual body segments for different cyclist positions

This study aims at investigating drag and convective heat transfer for cyclists at a high spatial resolution. Such an increased spatial resolution, when combined with flow-field data, can increase insight in drag reduction mechanisms and in the thermo-physiological response of cyclists related to heat stress and hygrothermal performance of clothing. Computational fluid dynamics (steady Reynolds-averaged Navier-Stokes) is used to evaluate the drag and convective heat transfer of 19 body segments of a cyclist for three different cyclist positions. The influence of wind speed on the drag is analysed, indicating a pronounced Reynolds number dependency on the drag, where more streamlined positions show a dependency up to higher Reynolds numbers. The drag and convective heat transfer coefficient (CHTC) of the body segments and the entire cyclist are compared for all positions at racing speeds, showing high drag values for the head, legs and arms and high CHTCs for the legs, arms, hands and feet. The drag areas of individual body segments differ markedly for different cyclist positions whereas the convective heat losses of the body segments are found to be less sensitive to the position. CHTC-wind speed correlations are derived, in which the power-law exponent does not differ significantly for the individual body segments for all positions, where an average value of 0.84 is found. Similar CFD studies can be performed to assess drag and CHTCs at a higher spatial resolution for applications in other sport disciplines, bicycle equipment design or to assess convective moisture transfer.     

Thermoregulation in rapid growing broiler chickens is compromised by constraints on radiative and convective cooling performance

Broiler chickens are selected to undergo a rapid six-week hatch-to-slaughter growth phase to attain large body and muscle mass. Broilers have relatively high resting and locomotor metabolic costs suggesting that adaptive thermoregulatory mechanisms are required to dissipate excess heat. Using thermal imaging in the growing broiler we characterised the trajectory of radiative and convective cooling in still air across broiler development. Scaling of head, tarsus and toe surface area did not deviate from body mass^2/3 while torso area increased with positive allometry, body mass^0.82, reflecting increased feather coverage and/or disproportionate abdominal/thoracic growth. Despite relatively increased area, the body became less effective for heat transfer presumably due to increasing feather coverage. Conversely, the magnitude of heat exchange from the distal hindlimbs was improved in larger birds. Overall capacity to transfer heat by convection and radiation in still air was attenuated over development, since the proportion of resting metabolic rate accounted for decreased in standing and sitting postures. This physiological constraint could be ameliorated by increased latent heat transfer or provision of environmental ventilation, which we modelled according to industrial guidelines. Based on models, higher airspeeds coincided with improved convective cooling that assisted in maintaining the proportion of RMR accounted for by convective and radiative heat transfer. These data highlight the potentially adverse thermoregulatory effects of rapid growth rate and body mass increases, which may contribute to the increased sedentary resting and decreased locomotor behaviour observed in large broilers.     

Shivering onset, metabolic response, and convective heat transfer during cold air exposure

The onset and intensity of shivering of various muscles during cold air exposure are quantified and related to increases in metabolic rate and convective heat loss. Thirteen male subjects resting in a supine position and wearing only shorts were exposed to 10 degrees C air (42% relative humidity and less than 0.4 m/s airflow) for 2 h. Measurements included surface electromyogram recordings at six muscle sites representing the trunk and limb regions of one side of the body, temperatures and heat fluxes at the same contralateral sites, and metabolic rate. The subjects were grouped according to lean (LEAN, n = 6) and average body fat (NORM, n = 7) content. While the rectal temperatures fluctuated slightly but not significantly during exposure, the skin temperature decreased greatly, more at the limb sites than at the trunk sites. Muscles of the trunk region began to shiver sooner and at a higher intensity than those of the limbs. The intensity of shivering and its increase over time of exposure were consistent with the increase in the convective heat transfer coefficient calculated from skin temperatures and heat fluxes. Both the onset of shivering and the magnitude of the increase in metabolic rate due to shivering were higher for the LEAN group than for the NORM group. A regression analysis indicates that, for a given decrease in mean skin temperature, the increase in metabolic rate due to shivering is attenuated by the square root of percent body fat. Thus the LEAN group shivered at higher intensity, resulting in higher increases in metabolic heat production and convective heat loss during cold air exposure than did the NORM group.     

Experimental study on convective heat transfer coefficient of the human body

1. 1. The convective heat transfer coefficient of the human body is essential to predict convective heat loss from the body.

2. 2. The object of this paper is to calculate the convective heat transfer coefficient of the human body using heat flow meters and to estimate the thermally equivalent sphere and cylinder to the human body.

3. 3. The experimental formulae of the convective heat transfer coefficient for the whole body were obtained by regression analysis for natural, forced and mixed convection.

4. 4. Diameters of the thermally equivalent sphere and cylinder of the human body were calculated as 12.9 and 12.2 cm, respectively.

Convective heat transfer measured directly with a heat flux sensor

A heat flux disk has been developed that directly measures the convective heat transfer in W/m2. When the sensor is calibrated on an aluminum cylinder, the calibration constant obtained is greatest in still air. As air movement increases, the calibration constant is reduced with increasing convective heat transfer coefficient, 0.5%.W-1.m2.K. The influence of wind on the calibration value is greatly reduced when the sensor is attached to a surface with lower thermal conductivity. The local convective heat transfer coefficient (hc) of the human body was measured. The leg acts in a manner similar to that of a cylinder, with the highest hc value at the front facing the wind and the lowest approximately 90 degrees from the wind, and in the wake a value is obtained that is close to the average hc value of the leg. When hc is measured at several angles and positions all over the body, the results indicate that the body acts approximately as a cylinder with a hc value related to the wind speed as hc = 8.6.v0.6 W.m-2.K-1, where v is velocity.     

A body temperature model for lizards as estimated from the thermal environment

A physically based model was built to predict the transient body temperature of lizards in a thermally heterogeneous environment. Six heat transfer terms were taken into account in this model: solar radiation, convective heat flow, longwave radiation, conductive heat flow, metabolic heat gain and respiratory energy loss. In order to enhance the model predictive power, a Monte Carlo simulation was employed to calibrate the bio-physical parameters of the target animal. Animal experiments were conducted to evaluate the calibrated body temperature model in a terrarium under a controlled thermal environment. To avoid disturbances of the animal, thermal infrared imagers were used to measure the land surface temperature and the body temperature. The results showed that the prediction accuracy of lizard's transient temperature was substantially increased by the use of Monte Carlo techniques (RMSE=0.59 °C) compared to standard model parameterization (RMSE=1.35 °C). Because the model calibration technique presented here is based on physical principles, it should be also useful in more complex, field situations.     

Parametric studies on the three-layer microcirculatory model for surface tissue energy exchange

The new three-layer microvascular mathematical model for surface tissue heat transfer developed in, which is based on detailed vascular casts and tissue temperature measurements in the rabbit thigh, is used to investigate the thermal characteristics of surface tissue under a wide variety of physiological conditions. Studies are carried out to examine the effects of vascular configuration, arterial blood supply rate, distribution of capillary perfusion, cutaneous blood circulation and metabolic heat production on the average tissue temperature profile, the local arterial-venous blood temperature difference in the thermally significant countercurrent vessels, and surface heat flux.     

Heat transfer in elephants: thermal partitioning based on skin temperature profiles

The elephant with its low surface-to-volume ratio presents an interesting problem concerning heat dissipation. To understand how such large mammals remain in thermal balance, we determined the major avenues of heat loss for an adult African elephant and an immature Indian elephant. Because conventional physiological measurements are difficult for these animals, the present study used a non-invasive technique, infrared thermography, to measure skin temperatures of each elephant. Detailed surface temperature profiles and surface area measurements of each elephant were used in standard equations for convective, conductive and radiant heat transfer. Results demonstrated that heat transfer by free convection and radiation accounted for 86% of the total heat loss for the elephants at T _a= 12·6 °C. Heat transfer across the ears, an important thermal window at high ambient temperatures, represented less than 8% of the total heat loss. Surface area of the animals, and metabolic heat production calculated from total heat loss of the African elephant, scaled predictably with body mass. In contrast, the thermal conductance of the elephants (71·6 W /°C, African; 84·5 W /°C, Indian) was three to five times higher than predicted from an allometric relationship for smaller mammals. The high thermal conductance of elephants is attributed to the absence of fur and appears to counteract reduced heat transfer associated with a low surface-to-volume ratio.     

An advanced computational bioheat transfer model for a human body with an embedded systemic circulation

In the present work, an elaborate one-dimensional thermofluid model for a human body is presented. By contrast to the existing pure conduction-/perfusion-based models, the proposed methodology couples the arterial fluid dynamics of a human body with a multi-segmental bioheat model of surrounding solid tissues. In the present configuration, arterial flow is included through a network of elastic vessels. More than a dozen solid segments are employed to represent the heat conduction in the surrounding tissues, and each segment is constituted by a multilayered circular cylinder. Such multi-layers allow flexible delineation of the geometry and incorporation of properties of different tissue types. The coupling of solid tissue and fluid models requires subdivision of the arterial circulation into large and small arteries. The heat exchange between tissues and arterial wall occurs by convection in large vessels and by perfusion in small arteries. The core region, including the heart, provides the inlet conditions for the fluid equations. In the proposed model, shivering, sweating, and perfusion changes constitute the basis of the thermoregulatory system. The equations governing flow and heat transfer in the circulatory system are solved using a locally conservative Galerkin approach, and the heat conduction in the surrounding tissues is solved using a standard implicit backward Euler method. To investigate the effectiveness of the proposed model, temperature field evolutions are monitored at different points of the arterial tree and in the surrounding tissue layers. To study the differences due to flow-induced convection effects on thermal balance, the results of the current model are compared against those of the widely used modelling methodologies. The results show that the convection significantly influences the temperature distribution of the solid tissues in the vicinity of the arteries. Thus, the inner convection has a more predominant role in the human body heat balance than previously thought. To demonstrate its capabilities, the proposed new model is used to study different scenarios, including thermoregulation inactivity and variation in surrounding atmospheric conditions.